“H ow he happened upon you on the way…” (Devarim 25:18)
The word karcha shares a root with the word kirur — to make cold.
After the miracles of Yetzias Mitzrayim and Kri’as Yam Suf all the nations of the world were trembling in fear. Amalek saw and heard as well but they remained unmoved. They attacked Bnei Yisrael an act that Rashi describes as “cooling off a boiling bathtub” so that other nations wouldn’t be scared to come and fight.
Such blatant indifference is the source of bad within the world and therefore Amalek must be completely eradicated. (Rav Chaim Shmuelevitz Sichos Mussar)